It is known that biphenyl compounds can be produced by various catalytic dehydrogenative dimerization of aromatic monocyclic compounds with molecular oxygen in the presence of a palladium-containing catalyst. However, it is also known that the conventional processes are disadvantageous in that the catalytic dehydrogenative dimerization results in production of a large amount of by-product having a high boiling point. This production of the by-product causes the yield of the resultant biphenyl compound and the percent selectivity to the biphenyl compound to become poor. Accordingly, it is desired to provide a new process for producing the biphenyl compounds from the aromatic monocyclic compounds at an excellent yield of the biphenyl compounds and percent selectivity to the biphenyl compounds.